4189
J . A m . Chem. SOC.1987, 109, 4189-4192
Metaphosphate and Tris(methy1ene)metaphosphate (P( CH&) Anions. Do They Have Three Double Bonds to Phosphorus? Andrzej Rajca,' Julia E. Rice, Andrew Streitwieser, Jr.,* and Henry F. Schaefer, III* Contribution from the Department of Chemistry, University of California, Berkeley, California 94720. Receiued August 25, 1986
Abstract: Ab initio studies are presented for metaphosphate ion, PO3- (l),and tris(methy1ene)metaphosphate ion, P ( C H 2 ) < (2). Using good basis sets at the SCF level, the minimum energy structure of 2 is a D3 structure with the CH2 groups twisted planar structure. Inclusion by 19' from the molecular plane, but this structure lies only 1 kcal mol-' below the constrained D,,, of electron correlation increases this energy difference by only 1 kcal mol-'. The charge distributions correspond to highly polar structures with large negative charges on the oxygens and methylene groups of PO3- and P(CH2)3-, respectively. The best simple representation of these compounds is as dipolar structures; double bonding to phosphorus is relatively weak.
Metaphosphate ion, PO3- ( l ) , and its methylene counterpart, P(CH& (2), present interesting problems in bonding and electronic structure. The least dipolar Lewis-type structure of 1, for example, is the hypervalent structure l a which formally requires
Table I. Relative Energies and P C Bond Lengths for 2 ( R H F / 3 - 2 1+ G * )
re1 energy. kcal mol-'
0.0 1 .o
0 3
o>p-oO/
-O\ /P -0
la
+--0
-0 \p2+-0-
-0/ lb
IC
expansion of the phosphorus octet, presumably with 3d orbitals. Three equivalent such structures could contribute to a resonance hybrid. An important alternative Lewis structure is the phosphonium dioxide structure l b in which all atoms have normal octets. Again, three equivalent such structures could contribute to a resonance hybrid. Structure l b emphasizes the potential availability on the central phosphorus of a 3p orbital that could be involved in a-bonding to the oxygens. In this respect this system differs from the phosphinate-type structures we studied previously2 in which four atoms are bonded to phosphorus. Finally, if multiple bonding is weak, structure IC is a highly polar Lewis structure with a phosphorus sextet similar in character to the carbonium oxide structure of a carbonyl compound, R,C+-O-. Metaphosphate ion plays an important role in biochemical mechanisms3 and is a stable gas-phase species," but has received only two previous a b initio s t ~ d i e s . ~The . ~ present paper also presents a detailed theoretical study of the trismethylene analogue 2. Structure 2a shows its formal relationship to l a . An important
D3h
C2a1 C2"12
13.4 42.1
O3613
1 12.0 62.4 1.16 5.98
c3c
&(30°) D3(40°)
P C bond length. 8, 1.672 1.672 1.667, 1.667, 1.703 1.651, 1.715, 1.715 1.725 1.756 1.672 1.674
Table 11. Geometriesu and Energies' for the Two Lowest Energy Structures 2-D3,,and 2-0, basis 3-21+G* DZ+P DZ+Pd 2-D3h
CH CP PCH
1.078 1.672 120.7
1.076 1.672 120.4
1.077 1.667 120.4
energy SCF CISD MP2
-455.535 923
-457.71 8 986' -458.216 197 -458.376 123
-457.736 483
2-D3 CH CP PCH HCPC
1.078 1.672 120.6 20.4
1.077 1.672 120.4 18.4
1.077 1.667 120.3 19.0
energy
HZC\ //P--CH2-
2a
distinction is that in 2 the energy effect of the relative mutual orientation of the methylene groups can provide an important gauge of the role of a-bonding. That is, as in the accompanying paper on hypophosphite ion,* the structural effects of relative orientations of the methylene groups provide a measure of the electronic effects of conjugation in these systems. The study of different methylene group orientations in 2 also provides a probe for the roles of Hiickel and Mobius conjugation in 1. Note that (1) Miller Institute Fellow, 1985-87. (2) Streitwieser, A,, Jr.; Rajca, A,; McDowell, R. S.; Glaser, R. J. Am. Chem. SOC.preceding paper in this issue. (3) Some recent references: Herschlag, D.; Jencks, W. P. J . Am. Chem. Sor. 1986, 108, 7938-46. Cussis, P. M.; Rous, A. J. Ibid. 1986, 108, 1298-1300. Ramirez, F.; Marecek, J.; Minore, J.; Srivastava, S.; Le Noble, W. Ibid. 1986, 108, 348-9. Recent reviews: Westheimer, F. H.; Calvo, Kim C. Stud. Org. Chem. (Amsterdam) 1983, 13, 261-75; Westheimer, F. H. ACS Symp. Ser. 1981, 171, 65-8 Chem. Rec;. 1981, 81, 313-326. (4) Henchman, M.; Viggiano, A. A.; Paulson, J. F.; Freedman, A,; Wormhoudt, J. J . Am. Chem. Sor. 1985, 107, 1453-5. (5) Loew, L. M.; MacArthur, W. R. J . Am. Chem. SOC.1977, 99, 1019-25. (6) O'Keeffe, M.;Domenges, B.; Gibbs, G. V . J . Phys. Chem. 1985, 89, 2304-9.
0002-786318711509-4189$01.50/0 ,
SCF CISD MP2
-455.537584
-457.720 150d -458.218 639 -458.379 827
-457.737 736
"All bond lengths in 8, and angles in degrees. 'In hartrees, with Davidson correction for unlinked clusters for C I S D . ' Z P V E = 16 804 cm-'. d Z P V E = 17 125 cm-'.
1 and 2 are also valence isoelectronic with trimethylenemethane dianion, the prototypical candidate for the putative Y aromaticit^.'-^ The synthesis and structure of a wbstituted derivative of 2 has recently been reported.1° Theoretical Approach 1 was studied theoretically with the first of the following basis sets; 2 was examined with all three. 1. 3-21+G* with sp-diffuse functions a t carbon (oxygen) and d functions a t all heavy atoms; the exponents were aSp(C) = 0.0438, a d ( P ) = 0.55, a d ( c ) = a d ( 0 ) = 0.8, asp(0)= 0.0845.'1~'2 (7) Agranat, I.; Skancke, A. J . Am. Chem. SOC.1985, 107, 867. (8) Gund, P. J . Chem. Educ. 1972, 49, 100-103. Finnegan, R. A. Ann. N . Y.Arad. Sci. 1969, 169, 242-266. Klein, J.; Medlik, A. J . Chem. SOC., Chem. Commun. 1973, 275-6. (9) Rajca, A.; Tolbert, L. M. J . Am. Chem. Sor. 1985, 107, 698. (10) Appel, R.; Gaitzsch, E.; Knoch, F. Angew. Chem., Inr. Ed. Engl. 1985, 24, 589-590.
0 1987 American Chemical Society
4190 J . Am. Chem. SOC.,Vol. 109, No. 14, 1987
-Y,
‘d
Figure 1. D, structure of 2.
This basis was used for both 1 and 2. 2. DZ+P, a d ~ u b l e - { ’ plus ~ polarization basis set, P(1 ls7pld/6s4pld), C ( 9 ~ 5 p l d / 4 ~ 2 p l dH(4slp/2slp), ), with polarization exponents q ( P ) = 0.5, ad(C) = 0.75, a p ( H ) = 0.75 (124 basis functions). 3. DZ+Pd, double-{ plus polarization plus diffuse functions, P( 12~8p2d/7sSp2d),C ( 10s6pld/5s3pld), H(4slp/2slp) with ad(P) = 1.0, 0.25 and the exponents of the diffuse functions, a,(C) = 0.0345, ap(C) = 0.0335, a,(P) = 0.0311, a,(P) = 0.0363, chosen according to the method suggested by Lee and Schaefer.I4 All geometries were optimized a t the RHF/3-21+G* level within the given symmetries and the constaint of planar methylene groups ( C H H P plane) (Table I) using analytical gradient techniques. The D , and planar D3h structures were also optimized with the D Z + P and DZ+Pd basis sets (Table 11). Harmonic frequencies were calculated for the D3 and D3hR H F / D Z + P structures using analytical second derivatives. Single-point energy calculations were performed for the R H F / D Z + P optimized structure with Moeller-Plesset (MP2) and configuration interaction (CI). The C I included all single and double excitations keeping the core orbitals doubly occupied and the corresponding virtual orbitals unoccupied; this procedure generated 105 176 configurations for Z-D3hand 198 025 configurations for 2-D3.
Metaphosphate Ion (1) The structure of 1 was optimized within D3hsymmetry to give a P-0 bond length of 1.475 A. Essentially the same structure was determined by O’Keeffe, Domenges, and Gibbs,6 using a 6-31G(*) basis (d orbitals on P only; no diffuse functions). The charge distribution was determined by “integrated spatial electron ~ by the natural populations” (ISEP),IScalculated with P R O J , ] and population (NP) procedure of Reed and Weinhold.” As mentioned in the previous paper2 the use of a projected density function ( 1 1) (a) Gordon, M. S.; Binkley, J. S.; Pople, J. A,; Pietro, W. J.; Hehre, W. J. J . Am. Chem. SOC.1982, 104, 2797. (b) Binkley, J. S.; Pople, J. A,; Hehre, W. J. [bid. 1980, 102, 939. (c) Francl, M. M.; Pietro, W. J.; Hehre, W. J.: Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (12) Spitznagel, G. W.; Clark, T.; Chandrasekhar, .J.; Schleyer, P. v. R . J . Comout. Chem. 1982, 3, 363. Chandrasekhar, J.; Andrade, J. G.; Schleyer, P.v. R-.J . Am. Chem. SOC.1981, 103, 5609. (13) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. Dunning, T. H.; Hay, P. J. Methods of Electron Structure Theory; Schaefer, H. F., 111, Ed.; Plenum Press: New York, 1977. (14) Lee, T. J.; Schaefer, H. F., 111. J . Chem. Phys. 1985, 83, 1784. (IS) Streitwieser, A,, Jr.; Collins, J. B.; McKelvey, J. M.; Grier, D.; Sender, J.; Toczko, A. G. Proc. Natl. Acad. Sci. USA 1979, 76, 2499. Collins, J. B.; Streitwieser, A,, Jr. J . Comput. Chem. 1980, 1 , 81. Grier, D. L.; Streitwieser, A,, Jr. J . Am. Chem. SOC.1982, 104, 3556. Streitwieser, A,, Jr.; Grier, D. L.; Kohler, B. A. B.; Vorpagel, E. R.; Schriver, G. W. Electron Distributions and the Chemical Bond, Coppens, P., Hall, M., Eds.; Plenum Press: New York, 1982. (16) Collins, J. B.; Streitwieser, A,, Jr.; McKelvey, J. M. Comput. Chem. 1979, 3, 79. (17) Reed, A. E.; Weinhold, F. J . Am. Chem. SOC.1985, 107, 1919.
Rajca et al. approximates the virial partitioning method of BaderI* and the resulting “ISEP” values are approximations to true spatial integrations over Bader “basins“; that is, the Bader method is based on rigorous and well-defined partitions of the electron density function, a physical observable, with assignment of the integrated electron populations to “atoms” that have rigorously defined boundaries by the Bader approach. The Reed and Weinhold N P method is a partition of the Hilbert space to “atomic orbitals”; since it is based on natural atomic orbitals and is relatively basis set independent, it is probably the “best” (most chemically mesningful) of this type of population analysis. ISEP and N P give the formal charge at oxygen as -1.56 and -1.23, respectively, and a t phosphorus +3.68 and +2.70, respectively. Such differences in magnitude are not uncommon in such comparison^^^ in which fundamentally different definitions are used for concepts that are not themselves physical observables. Much more important than the absolute numbers is the fact that both indicate a highly polar PO bond with, therefore, little double-bond character. The ISEP results for oxygen are similar to those obtained for phosphine oxide, -1 .56,20 phosphinate ion, H2P02-, -1.603, and methylenephosphoranyloxide ion, CH2PH20-, -1.624. The large charge separation in 1 suggests that any PO double bonding involved is highly polarized; such double bonding provides little charge transfer to phosphorus. A further indication that double bonding is weak comes from structure. The P O bond length of 1.47 8, in PO3- is about the same as that in phosphine oxide, 1.47 A,2o and is only 0.03 A shorter than that in H2P02-.2 In the latter two compounds any double bonding must be of the hypervalent type a t phosphorus. Thus, the availability of a 3p orbital on phosphorus in PO3- does not result in much bond shortening; the electronic structure is accordingly most simply represented by IC. These results for PO,- may be compared with those obtained recently for the neutral isoelectronic system (HN),PNH2.*I The P-NH bonds were described, primarily on the basis of Mulliken populations, as highly polar but with a significant *-bond contribution. Another related system is that of diimino- and dioxophosphorane, X2PH (X = N H , O).22 This system is a neutral analogue of 1 in which the comparable resonance structures are: -X-pH+=X X=pH+-X-X-pH2+-XThese compounds were also considered, primarily on the basis of Mulliken populations, to have highly polar electronic structures with only weak *-bonding. d-Orbitals were considered not to play a large role and then primarily to polarize the bonds.22 Note that the PO bond distance in dioxophosphorane, 1.435 A, is only 0.035 A shorter than that in PO,-, despite the comparison of a neutral molecule with an anion. Thus, the primary difference between our conclusions with regard to 1 and these related structures is one of degree. The integrated population results suggest even greater charge polarization and weaker *-bonding than suggested by Mulliken populations. The nature of this comparison requires further disc u ~ s i o n . Analysis ~~ can be focused, for example, on the charge distribution within the T system. PO3- has three occupied K valence MO’s (a2, MO 15, and e, MOs 18 and 19; the H O M O is MO 20) that correspond to the a:e4 TT configuration of a Yconjugated system. The two e MOs are nonbonding with nodes a t P (except for small contributions from d functions), whereas the a2-MO is a bonding M O to which the P 3p orbital can contribute. Mulliken population analysis of this MO, the only *bonding M O that corresponds to PO double bonding, assigns populations of P, 0.8, and 0,0.4. At first sight this analysis implies ~
~
~~
(18) Bader, R. F. W. Arc. Chem. Res. 1975, 8 , 34-40; 1985, 18, 9-15. Bader, R. F. W.; MacDougall, P. J. J . Am. Chem. SOC.1985, 107, 6788-95. Biegler-Koenig, F. W.; Bader, R. F. W.; Tang, T. H. J . Compuf. Chem. 1982, 3, 317-28. (19) Bachrach, S. M.; Streitwieser, A,, Jr., results to be published. (20) A number of computed results are summarized in: Streitwieser, A,, Jr.; McDowell, R. S.; Glaser, R. J . Comput. Chem., in press. (21) Ahlrichs, R.; Schiffer, H . J . Am. Chem. SOC.1985, 107, 6494-8. (22) Schoeller, W. W.; Lerch, C. Inorg. Chem. 1986, 25, 576-580. (23) We thank a referee whose detailed comments stimulated the following discussion.
J . A m . Chem. Soc., Vol. 109, No. 14, 1987 4191
Structure of Metaphosphates Table 111. Natural Populations (NP) for 1 and 2 (RHF/3-21+G*) total NP NAO populations 1
P
0
12.30
9.23
3PJP) 0.56
I
2PJO) 1.79
NAO
total NP P 2
13.33 13.30 Dih 13.35 ClrI C z C l 2 13.37 D3,,L3 14.38 14.16 C3& D1
-P
0
populations
c
c
c
3P-P)
2PJQ
7.34 7.35 7.45 6.99 6.89 6.98
7.34 7.35 7.21 7.48 6.89 6.98
7.34 7.35 7.27 7.48 6.89 6.98
0.89 0.88 0.86 0.80 1.81
1.69 1.56 1.20
normal double bonding and disagrees with the conclusions above; however, such an interpretation is greatly oversimplified. Note that the basis set does not include a “3p” orbital; there are only 2p-type functions with varying degrees of diffuseness. A large part of the P pn population comes from the core p function required to make the valence a-MO orthogonal to the formal 2p, core. The core function is too compact (and has the wrong sign!) to contribute to *-bonding. Another contribution to the P pZ orbital comes from a diffuse p function that is used in part to describe electrons close to the oxygens and assigned in this manner by the Mulliken procedure to phosphorus, This discussion emphasizes the point that Mulliken populations are basis set populations, and basis sets are generally not equivalent to orthonormal atomic orbitals. This objection does not apply to the natural atomic orbital (NAO) occupancies obtained by the method of Reed and Weinhold.” Some N A O occupancies for PO3- are summarized in Table 111. Note that the 3p, occupancy is only 0.56 e. This result is graphically affirmed by the planar electron density plot of the a2 MO, the only a - M O to which the phosphorus px orbitals can contribute, in Figure 2a. This plot is that of the electron density in a plane along a P O bond and perpendicular to the molecular plane. Note that, unlike the first-row all-carbon analogue trimethylenemethane, in which the central carbon pT orbital dominates, the central phosphorus contribution in Figure 2a is rather small; the density maximum at P is less than half that at 0. The ISEP value at each 0 in this MO is 0.49 e, or a residual px population on P of 0.52 e, a value close to that of the NAO population. Figure 2a shows that there is some a-bonding between P and 0;the highest contour encompassing both atoms has the relatively low value of 0.019. Finally, the total a-electron projection plot (MOs, 15, 18, and 19) in Figure 2b shows further the pronounced polarization of electrons from P to 0. Note that phosphorus formally contributes 2 e to these P MOs and the oxygens contribute 4. Not all of the phosphorus electrons are transferred to the oxygens; accordingly the contributioii of the phosphorus pT orbital is, as indicated above, not zero, but its contribution is relatively small.
Tris(methy1ene)metaphosphate Ion (2) Six structures were optimized at the R H F level of theory using the 3-21+G* basis set within given symmetry constraints and holding the carbons and phosphorus in a single plane. The corresponding global minimum is D, symmetric (2-0,) with a PC bond length of 1.672 A and with the methylene groups twisted in a propeller manner by 20’ with respect to the PC3 plane (Figure I). Reoptimization of the lowest energy structure using the larger basis sets DZ+P and DZ+Pd changes the structure but little; in particular, the PC bond lengths are essentially identical and show a good agreement with the X-ray value (1.69 A) of the knownIO derivative of 2 (Table 11). The DZ+P harmonic vibrational frequencies indicate that 2-D3 is a minimum (all frequencies are real). The lowest frequency, which is doubly degenerate and corresponds to twisting of the methylene groups, is fairly small (340 cm-I); that is, the potential energy surface is rather flat with respect to this particular normal mode. Indeed, the D3h-symmetric structure (“all-in-plane”) (Z-D,,,), which is a transition structure for the CH,-twist (one imaginary frequency, i260 cm-I), is only
Figure 2. (a) Planar density of MO 15 of 18 3-21+G*, for a plane containing the PO bond and perpendicular to the molecular plane. Contour levels are 0.01 to 0.1 by 0.01 e au-’. (b) Projected density plot of r-MO system of 1 (MOs 15, 18, 19) for the molecular plane. Contour levels are 0.1 to 0.8 by 0.1 e 8u-l.
about 1 kcal mol-’ higher at the R H F level of theory (all three basis sets). Single-point CISD calculations using the DZ+P basis set give an energy difference (D3h - 0 , ) of 1.5 kcal mol-’ and, after Davidson c o r r e c t i ~ n gives , ~ ~ 1.9 kcal mol-’, comparable to the MP2 result of 2.3 kcal mol-’. The final value for this energy difference is 1.0 (CI) or 1.4 kcal mol-’ (MP2) after zero-point vibrational energy correction, essentially identical with that of our lowest level theoretical approach (RHF/3-21 +G*). This result invites the following interpretation. If a-bonding were important in this type of compound, a and a * orbitals would have a larger energy difference in the planar D3h structure than in a structure with twisted methylene groups. Accordingly, C I would be more important for the latter structure and inclusion of CI should increase the energy difference significantly. The observed result of a small effect of CI on this energy difference then suggests that a-bonding in this compound is of minor importance. The shallow bending potential for 0, twisting of the methylene groups was confirmed by additional calculations in which the twisting angle was set at 30 and 40’. These D, structures have energies only 1.16 and 5.98 kcal mol-’, respectively, above the global minimum and virtually unchanged PC bond lengths. This shallow potential provides further evidence that PC a-bonding is relatively weak. Although the symmetrical twisting of three methylene groups (2-D3h 2-0,) requires relatively little energy,
-
~
~
(24) Langhoff, S . R.; Davidson, E. R. Int. J . Quant. Chem. 1974, 8, 61.
4192 J . Am. Chem. Soc., Vol. 109, No. 14, 1987
P
C
-
--
llTlllllllllilllllllllllllllllilllilllllllllllllllllllllllllllll
Rajca et al. kcal mol-’ relatively to 2-D3h. Pyramidalization at the phosphorus within the C3, symmetry constraint (2-C3J inevitably lowers the energy of the “free electron pair a t P” M O which now becomes the subjacent HOMO. The CC distances also decrease to further favor Mobius resonance. Consequently, the 2-C3, structure is about 50 kcal mol-’ below 1 - & 1 3 (3-21+G*, Table I ) . The unimportance of Mobius conjugation in 2 suggests that it is equally unimportant in 1. Moreover, the greater electronegativity of oxygen compared to carbon makes the PO bond in PO3- more polar than the PC bond in 2. This point shows up in the higher P 3p, N A O population summarized in Table 111. The present results may be compared with recent calculations on the related neutral system bis(methylene)phosphorane, (CHz)2PH.25The a system was described as strongly polarized but less so than in H P 0 2 (vide supra). The weakness of the R bonds was indicated by a distinct tendency toward pyramidalization around phosphorus. This interpretation, which again is based largely on Mulliken population analyses, is nevertheless consistent with our results for 2. Finally, we may ask why the methylene groups in 2 are twisted at all. The hydrogens on different methylene groups in planar 2 are separated by 2.9 A, substantially outside the sum of their van der Waals radii; hence, steric effects are unlikely to be important. We suggest that the entire structure is dominated by simple Coulombic effects. The large negative charges need to stay as close as possible to the positive phosphorus but to stay mutually apart. Slight twisting moves the carbanion lobes farther apart, but additional twisting gets upper and lower lobes of two methylene groups too close. Maximum repulsion is reached at the 2-D3h13 structure; the close carbanion lobes in this structure account for its high energy. Conclusion The double-well potential energy surface of 2 with the D3 structure as minimum and the D3hstructure a t the top of the barrier underscores the weakness of the phosphorus-carbon 3p,-2p, overlap; the P C bond in 2 is ylide-like. This conclusion is confirmed by the small calculated effect of CI on the energy difference between the planar D3h and twisted D3 structures. Together with the charge distribution analysis, these results indicate dipolar structures for PO3- and P(CH2)3- in which phosphorus-oxygen and phosphorus-carbon double bonding is relatively weak and dominated by Coulombic effects. Acknnwledgment. This research was supported in part by Air Force Office of Scientific Research Grant No. AFOSR 82-01 14 (to A S . ) and by National Science Foundation Grant No. CHE8218785 (to H.F.S.). (25) Schoeller, W. W.; Niemann, J. J . Am. Chem. SOC.1986, 108, 22-6.
